Approximately two thirds of PA programs require the GRE, so not taking the test will limit your application options, but it will not prevent you from going to PA school.
The exam is scheduled, computerized, takes approximately three to four hours (timed), and consists of three parts - verbal, essays, and math. It scored like the SAT used to be, meaning that the maximum score for each section (verbal and math) is 800 - a perfect score being 1600. Essays take about three weeks to grade, and are scored on a scale of zero to six, with six being the best.
In high school we all stressed about having the best SAT scores - fortunately, the pressure isn't as big for PA programs. Some of these schools only require the GRE because the university requires it for admission as a graduate student. Other programs look at it similarly to your GPA's. As a general rule of thumb, aim for a score of at least 1000, but of course, higher scores are better and give you greater peace of mind. I strongly recommend that you retake the GRE if you score less than 1000.
Don't worry about it too much, though. By virtue of being accepted to BYU, you have demonstrated academic aptitude sufficent to do decently on the GRE. Also, having an "average" GRE score will NOT ruin your application if you have decent grades, work expreience, essay, letters of recommendation, and so forth. It is only a part of your entire application.
But do worry a little. For a sciences major, the worst thing about the exam will probably be the verbal section. Basically, they are testing whether or not you memorized their extensive list of extremely obscure words. You would be wise to purchase a GRE-prep book and spend some time familiarizing yourself with the word lists and word root lists. Make sure to freshen up on your algebra, geometry, and especially statistics.
If you take the test and are displeased with your score, you are allowed to retake the test multiple times.
For more information, please visit www.ets.org/gre.